ON $\epsilon$-APPROXIMATE SOLUTIONS FOR CONVEX SEMIDEFINITE OPTIMIZATION PROBLEMS

An Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

-Duality Theorems for Convex Semidefinite Optimization Problems with Conic Constraints

Optimality conditions for approximate solutions of vector optimization problems with variable ordering structures

‎We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces‎. ‎Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...

an interior point algorithm for solving convex quadratic semidefinite optimization problems using a new kernel function

in this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual interior point method (ipm) based on a new kernel function with a trigonometric barrier term. iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. although our proposed kernel function is neither a self-regular (sr) function nor logarithmic barrier ...

A Hybrid Algorithm for Convex Semidefinite Optimization

We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general largescale semidefinite programs and hence can be readily applied to a variety of machine learning problems. We show experimental results on three machine learning problems. Our approach ou...